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Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation

Author

Listed:
  • Junwei Cheng

    (School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China)

  • Xiang Tian

    (School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China)

Abstract

In this paper, we prove that the isospectral flows associated with both the x -part and the n -part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these two hierarchies of symmetries are equivalent. Additionally, we construct the non-isospectral flows associated with the x -part of the Lax pair, which can be interpreted as the master symmetries of the semi-discrete lattice potential Korteweg–de Vries equation.

Suggested Citation

  • Junwei Cheng & Xiang Tian, 2024. "Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation," Mathematics, MDPI, vol. 13(1), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:117-:d:1557219
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    References listed on IDEAS

    as
    1. Senyue Lou, 2024. "Progresses on Some Open Problems Related to Infinitely Many Symmetries," Mathematics, MDPI, vol. 12(20), pages 1-18, October.
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